New York Governor Andrew Cuomo — who has come under criticism from some LGBT advocates for not personally doing more to legalize same-sex marriage in the state — has just released a new video likening the fight for marriage quality to the struggle for civil rights and women’s suffrage and calling on New Yorkers to pressure their elected representatives to vote “yes” on marriage:

CUOMO: Same-sex couples are denied rights that other New Yorkers take for granted. Same-sex couples are denied over 1,000 federal and 700 state rights that are afforded to millions of others. Rights as basic as being able to visit the person you love in the emergency room, the opportunity to love and care for one another, the freedom to express their life-long commitment and the basic dignity of having that relationship recognized by the state they call home. This is a matter of fairness and equality. It is not a question of religion or culture, but a question of legal rights and government policy….Marriage equality is the next chapter in our civil rights story.

As the Wall Street Journal’s Jacob Gershman notes, Cuomo is also stepping up his personal lobbying, holding “private talks—in person and on the phone—with Republicans and Democrats in the Senate who represent the crucial swing votes for passage.”

Meanwhile, over the weekend, Republican state Sen. James Alesi — who voted against marriage in 2009 — “appeared at a major upstate dinner held by the state’s biggest gay-rights group” signaling that he may consider changing his vote on this time around. “Having Alesi there was seen as an important development since the dinner was all about marriage equality,” a prominent Democrat and gay-rights activist told The New York Post.

Supporters seemed to have made an agreement not to move ahead with marriage equality until Senate votes are secured, however. If the vote were held today, the measure would likely fall approximately six votes short of passage.